The grades on a physics midterm at Covington have an average of μ=72 and σ=2.0 If Stephanie scored 1.23 standard deviations above the mean.

a. What score did Stephanie get on the exam?
b. What percent of students scored better than Stephanie?

a) She scored 74.46 on the exam.

b) 11% of the students scored better than Stephanie.

Step-by-step explanation:

The z-score measures how many standard deviation a score X is above or below the mean. It is given by the following formula:

In which is the mean and is the standard deviation.

In this problem, we have that:

a. What score did Stephanie get on the exam?

Stephanie scored 1.23 standard deviations above the mean. This means that her z-score is

We want to find X

She scored 74.46 on the exam.

b. What percent of students scored better than Stephanie?

Each z-score has a pvalue, which is the percentile of the score. We look this pvalue at the z table.

has a pvalue of 0.89.

This means that Stephanie's score is in the 89th percentile, which means that she scored more than 89% of the students and scored less than 100-89 = 11% of the students.

So 11% of the students scored better than Stephanie.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.